I am fairly sure I have a bad O2 sensor or at least a bad connection. It runs in open loop at idle.

I get codes 0305 and P0132 (O2 sensor circuit high voltage (bank 1, sensor 1) Front sensor LH bank short circuit to battery supply)

Does this seem right and do I need to replace O2 sensors in pairs?

 

you dot have to change both. If you prefer changing both, that should be fine as well. Fix the problem side first, if you mess up with the other side, youll be fixing more stuff.